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An Example of Interaction Between Finite-Amplitude Gravity Waves

David D. HoughtonUniversity of Washington, Seattle, Wash.

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Abstract

An incompressible, stratified, hydrostatic, inviscid fluid model is used to demonstrate non-linear effects in the interaction of finite amplitude gravity waves. A statically stable density stratification is approximated by the superposition of ten homogeneous fluid layers with a very deep layer on top. Computations are made using a two-step Lax-Wendroff finite difference system. The solutions reveal intrawave distortions comparable to those predicted by analytical studies of one- and two-layer fluid models. During the interaction of two waves, the solutions show overall changes in wave speed which are of the same magnitude as the variations in wave speed that cause the intrawave distortions. These changes are related differently to the horizontal fluid velocities in the waves.

Abstract

An incompressible, stratified, hydrostatic, inviscid fluid model is used to demonstrate non-linear effects in the interaction of finite amplitude gravity waves. A statically stable density stratification is approximated by the superposition of ten homogeneous fluid layers with a very deep layer on top. Computations are made using a two-step Lax-Wendroff finite difference system. The solutions reveal intrawave distortions comparable to those predicted by analytical studies of one- and two-layer fluid models. During the interaction of two waves, the solutions show overall changes in wave speed which are of the same magnitude as the variations in wave speed that cause the intrawave distortions. These changes are related differently to the horizontal fluid velocities in the waves.

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